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skullpatrol

Does 0.999...=1?

  • one year ago
  • one year ago

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  1. zzr0ck3r
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    .9999........ is not a number

    • one year ago
  2. zzr0ck3r
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    have you taken calculus?

    • one year ago
  3. zzr0ck3r
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    http://www.math.com/school/subject2/lessons/S2U2L1DP.html

    • one year ago
  4. zzr0ck3r
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    scroll down to number 4, its actaully an easy proof.

    • one year ago
  5. zzr0ck3r
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    you will enjoy calculus:)

    • one year ago
  6. carson889
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    Here is an algebraic proof of it: 10x = 9.999999... with x = 0.99999... 10x - x = 9.99999... - 0.999999... 9x = 9 Thus, x = 1

    • one year ago
  7. zzr0ck3r
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    This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

    • one year ago
  8. zzr0ck3r
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    there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

    • one year ago
  9. ByteMe
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    wait... doesn't 0.9999... = 9/10 + 9/100 + 9/1000 + .... an infinite bounded series?

    • one year ago
  10. mayankdevnani
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    The number "0.9999..." can be "expanded" as: 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

    • one year ago
  11. mayankdevnani
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    • one year ago
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  12. mayankdevnani
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    • one year ago
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  13. zzr0ck3r
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    lol, read this. then you will see the point of the question http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

    • one year ago
  14. mayankdevnani
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    So the formula proves that 0.9999... = 1.

    • one year ago
  15. mayankdevnani
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    @skullpatrol ok

    • one year ago
  16. zzr0ck3r
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    but .99999...is not a number is the point of this topic

    • one year ago
  17. mayankdevnani
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    0.999999..... is a no. we have tp prove that it is equal to 1

    • one year ago
  18. mayankdevnani
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    *to

    • one year ago
  19. zzr0ck3r
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    its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

    • one year ago
  20. zzr0ck3r
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    its not a finite number.... it can be looked at as a sequence....at infinity then its a number. I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

    • one year ago
  21. zzr0ck3r
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    Its an extended real number in the since that infinity is an extended real number....

    • one year ago
  22. mayankdevnani
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    "But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

    • one year ago
  23. zzr0ck3r
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    right and i dont think he has had calculus...

    • one year ago
  24. zzr0ck3r
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    this started with density of rational/irational and archimedes principle on the real line

    • one year ago
  25. zzr0ck3r
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    the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

    • one year ago
  26. mayankdevnani
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    hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

    • one year ago
  27. mayankdevnani
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    right?? @zzr0ck3r

    • one year ago
  28. zzr0ck3r
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    This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

    • one year ago
  29. zzr0ck3r
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    right:)

    • one year ago
  30. mayankdevnani
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    :)

    • one year ago
  31. waterineyes
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    0.9999 is approximately equal to 1 but it is not exactly equal.. \[0.999 \approx 1 \qquad \qquad (0.999 \ne 1)\]

    • one year ago
  32. mayankdevnani
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    got it @skullpatrol

    • one year ago
  33. mayankdevnani
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    this question...lol

    • one year ago
  34. mayankdevnani
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    http://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml

    • one year ago
  35. Zarkon
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    can you provide a proof of this ... "This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

    • one year ago
  36. zzr0ck3r
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    no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0-infinity

    • one year ago
  37. Zarkon
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    your teacher is either wrong or you have misquoted her

    • one year ago
  38. Zarkon
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    the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

    • one year ago
  39. ParthKohli
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    \[1 - 0.999\cdots = 0.000\cdots = 0\]

    • one year ago
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